L.13- Ray Diagrams

Optical Systems: Objects and Images Discussion

Overview of Real and Virtual Objects and Images

• Real Objects vs. Virtual Objects:

  • Real objects emit diverging light, resulting in negative vergence.

  • Virtual objects result from converging light entering the optical system, indicating a real object was positioned elsewhere.

Light Behavior in Optical Systems

• Light entering can be diverging or converging.

• Diverging Light:

  • Emitted from real objects.

  • Denoted by negative vergence.

  • Variables:

  • Capital U (Light entering the system) = -

  • Object distance (u) = -

  • Real objects are positioned on the left side (negative side) of optical diagrams.

• Converging Light:

  • Associated with virtual objects.

  • Denoted by positive vergence.

  • Variables:

  • Capital U (Light entering the system) = +

  • Object distance (u) = +

  • Virtual objects are positioned on the right side (positive side) of diagrams.

Definitions and Important Concepts

• Image Formation:

  • A real image can be projected onto a screen, formed by converging light, always located on the right side of the optical system, corresponding to positive values of image distance (v).

  • A virtual image cannot be projected onto a screen, resulting from diverging light, with negative values of image distance (v), found on the left side.

• Vergence Relationships:

  • Formula linking vergence entering and exiting the optical system:

  • U + D = B where:

    • U = vergence of light entering the optical system.

    • D = power of the optical system.

    • B = vergence of light exiting the optical system.

• Lens Formula:

  • \frac{n1}{u} + v = \frac{n2}{v}

  • Where:

  • n1 = index of refraction on the left side.

  • n2 = index of refraction on the right side.

  • u = object distance.

  • v = image distance.

  • Signs are crucial: left = negative, right = positive.

Cardinal Points of Optical Systems

• Primary Focal Point (F1):

  • Light traveling through [F_1] gets refracted and exits parallel to the optical axis.

  • To find: F1 = -\frac{n1}{D}

• Secondary Focal Point (F2):

  • Light arriving parallel to the optical system exits through [F_2].

  • To find: F2 = \frac{n2}{D}

• Nodal Point (N):

  • Center of curvature.

  • For thin lenses, it's located at the intersection of the lens with the optical axis.

Ray Tracing Techniques

• When tracing rays:

  1. Draw the optical axis and lens.

  2. Identify cardinal points (F1, F2, N).

  3. Draw three predictable rays:

  • Nodal Ray: passes straight through the nodal point (N).

  • Ray through F1: converges after reaching lens.

  • Ray parallel to optical axis: through F2 and continues onward.

Determining Image Characteristics

• From ray intersection points:

  • If rays converge on the right, the image is real and inverted.

  • If rays diverge and traced backwards lead to the left, the image is virtual and upright.

Example Calculations and Scenarios

• Example: Convex lens with real object:

  • If an object is 50cm from a +4 D lens, find Focal Points:

  • F1 Calculation: [F_1 = -\frac{1}{4} = -0.25 m]

  • F2 Calculation: [F_2 = \frac{1.5}{4} = 0.375 m]

  • Use ray diagrams to determine image distance (v) and magnification (M).

• Example: Virtual object and convex lens:

  • Determine if virtual images form in different configurations (real object closer than focal length).

Complex Scenarios with Concave Lenses

• Concave lenses reverse positions of focal points.

• Calculate image characteristics using similar principles and techniques applied above.

Practical Applications

• Understanding the principles helps in various optical technologies, from lenses to cameras and eyewear.

Mathematical Relationships in Image Formation

• Magnification (M) formula:

  • M = \frac{u}{v}

  • Interpret signs: positive = upright, negative = inverted.

Conclusion

• Mastering ray tracing and understanding object-image relationships enhances comprehension of optics for practical use in real-world applications.